Let's take an American supercarrier like the Nimitz class as an example. During peacetime, its number of fixed-wing fighters is about 50, and this will probably rise to 80-100 in wartime. Let's use the F/A-18 Superhornet as an example: it should have about 8,000 kg of weapons payload and possibly around 10-12 external hardpoints (don't have specific number on hand, but it is certainly around that). If that gets outfitted heavily for anti-ship purposes, it can carry probably around 4 anti-ship missiles (LRSAM weighs about 1,000 kg without boosters), and the remainder being air-to-air missiles. This suggests that if all FA-18s were scrambled quickly, it can muster around 800-1000 missiles at the point in time, with about 320-400 of these being anti-ship. This missile count is not significantly different to a group of destroyers that is roughly equivalent to the construction cost of the Nimitz supercarrier and airwing (something like $18-$20 billion). This roughly translates to about 10 Arleigh Burkes. Once the FA-18s completed their mission, they will return to their carrier and probably need some time to reload and service before they can sortie again.
Once the destroyers fired all their missiles though, they are kind of done. The Flight IIA+ Burkes do not have a crane onboard to reload the VLS, and from my understanding reloading is done in port. But the carrier aircrafts can come back for round 2, and then round 3, and so on, given enough time in a protracted engagement or stanbdoff. So, I'd say the carrier has more sustaining power than 10 destroyers, and this is probably where the '3,000 missile vs 1,000' firepower analogy comes in.
There's other advantages to the carrier, like a greater effective striking range for its anti-ship weapon relative to the destroyer. But I'm sure there are advanatages to the destroyer too.
